1. ESTIMATION OF RESERVOIR TEMPERATURES
The evaluation of the reservoir temperatures for geothermal systems is made in terms of GEOTHERMOMETRY APPLICATIONS

2. WATER CHEMISTRY
Chemical composition of waters is expressed in terms of major anion and cation contents.
Major Cations: Na+, K+, Ca++, Mg++
Major Anions: HCO3- (or CO3=), Cl-, SO4=
HCO3-  dominant in neutral conditions
CO3=  dominant in alkaline (pH>8) conditions
H2CO3  dominant in acidic conditions
Also dissolved silica (SiO2) in neutral form
as a major constituent
Minor constituents: B, F, Li, Sr, ...

3. CHEMICAL GEOTHEROMOMETERS
PART I. Basic Principles &Types

4. TYPES OF CHEMICAL GEOTHERMOMETERS
SILICA GEOTHERMOMETERS
CATION GEOTHERMOMETERS (Alkali Geothermometers)

5. SILICA GEOTHERMOMETERS
based on the
experimentally determined
temperature dependent
variation in the solubility of silica in water
Since silica can occur in various forms in geothermal fields (such as quartz, crystobalite, chalcedony, amorphous silica) different silica geothermometers have been developed by different workers

6. SILICA GEOTHERMOMETERS
Equation
Reference
Quartz-no steam loss
T = 1309 / (5.19 – log C)
Fournier (1977)
Quartz-maximum steam loss at 100 oC
T = 1522 / ( log C)
Quartz
T = C x 10-4 C x 10-7 C log C
Fournier and Potter (1982)
T = C x 10-4 C x 10-7 C log C
Arnorsson (1985) based on Fournier and Potter (1982)
Chalcedony
T = 1032 / ( log C)
T = 1112 / ( log C)
Arnorsson et al. (1983)
Alpha-Cristobalite
T = 1000 / ( log C)
Opal-CT
(Beta-Cristobalite)
T = 781 / ( log C)
Amorphous silica
T = 731 / ( log C)

7. SILICA GEOTHERMOMETERS
The followings should be considered :
temperature range in which the equations are valid
effects of steam separation
possible precipitation of silica
before sample collection
(during the travel of fluid to surface, due to silica oversaturation)
after sample collection
(due to improper preservation of sample)
effects of pH on solubility of silica
possible mixing of hot water with cold water

8. SILICA GEOTHERMOMETERS
Temperature Range
silica geothermometers are valid for temperature ranges up to 250 C
above 250C, the equations depart drastically from the experimentally determined solubility curves

9. SILICA GEOTHERMOMETERS Temperature Range
Fig.1. Solubility of quartz (curve A) and amorphous silica (curve C) as a function of temperature at the vapour pressure of the solution. Curve B shows the amount of silica that would be in solution after an initially quartz-saturated solution cooled adiabatically to 100 C without any precipitation of silica (from Fournier and Rowe, 1966, and Truesdell and Fournier, 1976).
At low T (C) 
qtz less soluble
amorph. silica more soluble
Silica solubility is controlled by amorphous silica at low T (C) quartz at high T (C)

10. SILICA GEOTHERMOMETERS Silica Precipitation
SiO2 
Temperature Estimate
e.g.
T = 1309 / (5.19 – log C)
C = SiO2 in ppm
decrease in C (SiO2 in water < SiO2 in reservoir)
increase in denominator
decrease in T

11. SILICA GEOTHERMOMETERS Effect of Mixing
Hot-Water  High SiO2 content
Cold-Water  Low SiO2 content
(Temperature  Silica solubility )
Mixing (of hot-water with cold-water)
Temperature
SiO2 
Temperature Estimate 
e.g.
T = 1309 / (5.19 – log C)
C = SiO2 in ppm
decrease in C
increase in denominator of the equation
decrease in T

12. SILICA GEOTHERMOMETERS
Process Reservoir Temperature
Steam Separation  Overestimated
Silica Precipitation  Underestimated
Increase in pH  Overestimated
Mixing with cold water  Underestimated

13. CATION GEOTHERMOMETERS (Alkali Geothermometers)
based on the partitioning of alkalies between solid and liquid phases
e.g. K+ + Na-feldspar = Na+ + K-feldspar
majority of are empirically developed geothermometers
Na/K geothermometer
Na-K-Ca geothermometer
Na-K-Ca-Mg geothermometer
Others (Na-Li, K-Mg, ..)

14. CATION GEOTHERMOMETERS Na/K Geothermometer
Fig.3. Na/K atomic ratios of well discharges plotted at measured downhole temperatures. Curve A is the least square fit of the data points above 80 C. Curve B is another empirical curve (from Truesdell, 1976). Curves C and D show the approximate locations of the low albite-microcline and high albite-sanidine lines derived from thermodynamic data (from Fournier, 1981).

15. CATION GEOTHERMOMETERS Na/K Geothermometer
Equations
Reference
Na-K
T=[855.6/(0.857+log(Na/K))]
Truesdell (1976)
T=[833/(0.780+log(Na/K))]
Tonani (1980)
T=[933/(0.993+log (Na/K))]
( oC)
Arnorsson et al. (1983)
T=[1319/(1.699+log(Na/K))]
( oC)
T=[1217/(1.483+log(Na/K))]
Fournier (1979)
T=[1178/(1.470+log (Na/K))]
Nieva and Nieva (1987)
T=[1390/(1.750+log(Na/K))]
Giggenbach (1988)

16. CATION GEOTHERMOMETERS Na/K Geothermometer
gives good results for reservoir temperatures above 180C.
yields erraneous estimates for low temperature waters
temperature-dependent exchange equilibrium between feldspars and geothermal waters is not attained at low temperatures and the Na/K ratio in these waters are governed by leaching rather than chemical equilibrium
yields unusually high estimates for waters having high calcium contents

17. CATION GEOTHERMOMETERS Na-K-Ca Geothermometer
Equations
Reference
Na-K-Ca
T=[1647/ (log (Na/K)+  (log (Ca/Na)+2.06)+ 2.47)]
a) if logCa/Na)+2.06 < 0, use =1/3 and calculate TC
b) if logCa/Na)+2.06 > 0, use =4/3 and calculate TC
c) if calculated T > 100C in (b), recalculate TC using =1/3
Fournier and Truesdell (1973)

18. CATION GEOTHERMOMETERS Na-K-Ca Geothermometer
Works well for CO2-rich or Ca-rich environments provided that calcite was not deposited after the water left the reservoir
in case of calcite precipitation
Ca 
1647
T =
log (Na/K)+  (log (Ca/Na)+2.06)+ 2.47
Decrease in Ca concentration (Ca in water < Ca in reservoir)
decrease in denominator of the equation
increase in T
For waters with high Mg contents, Na-K-Ca geothermometer yields erraneous results. For these waters, Mg correction is necessary

19. CATION GEOTHERMOMETERS Na-K-Ca-Mg Geothermometer
Equations
Reference
Na-K-Ca-Mg
T = TNa-K-Ca - tMgoC
R = (Mg / Mg Ca K) x 100
if R from 1.5 to 5
tMgoC = log R (log R)2 – (log R)2 / T x 107 log R / T2
if R from 5 to 50
tMgoC= log R (log R) x105(log R)2/T-1.968x107(log R)3/T2
Note: Do not apply a Mg correction if tMg is negative or R<1.5.
If R>50, assume a temperature = measured spring temperature.
T is Na-K-Ca geothermometer temperature in Kelvin
Fournier and Potter (1979)

20. UNDERGROUND MIXING OF HOT AND COLD WATERS
Recognition of Mixed Waters
Mixing of hot ascending waters with cold waters at shallow depths is common.
Mixing also occurs deep in hydrothermal systems.
The effects of mixing on geothermometers is already discussed in previous section.
Where all the waters reaching surface are mixed waters, recognition of mixing can be difficult.
The recognition of mixing is especially difficult if water-rock re-equilibration occurred after mixing (complete or partial re-equilibration is more likely if the temperatures after mixing is well above 110 to 150 C, or if mixing takes place in aquifers with long residence times).

21. UNDERGROUND MIXING OF HOT AND COLD WATERS
Some indications of mixing are as follows:
systematic variations of spring compositions and measured temperatures,
variations in oxygen or hydrogen isotopes,
variations in ratios of relatively *conservative elements that do not precipitate from solution during movement of water through rock (e.g. Cl/B ratios).

22. SILICA-ENTHALPY MIXING MODEL
Dissolved silica content of mixed waters can be used to determine the temperature of hot-water component .
Dissolved silica is plotted against enthalpy of liquid water.
Although temperature is the measured property, and enthalphy is a derived property, enthalpy is used as a coordinate rather than temperature. This is because the combined heat contents of two waters are conserved when those waters are mixed, but the combined temperatures are not.
The enthalpy values are obtained from steam tables.

23. SILICA-ENTHALPY MIXING MODEL
Fig. 5. Dissolved silica-enthalpy diagram showing procedure for calculating the initial enthalpy (and hence the reservoir temperature) of a high temperature water that has mixed with a low temperature water (from Fournier, 1981)

24. SILICA-ENTHALPY MIXING MODEL
A = non-thermal component
(cold water)
B, D = mixed, warm water
springs
C = hot water component at
reservoir conditions
(assuming no steam
separation before mixing)
E = hot water component at
(assuming steam separation
before mixing)
Boiling
T = 100 C
Enthalpy = 419 J/g
(corresponds to D in the graph)
Enthalpy values (at corresponding temperatures)
are found from Steam Table in Henley et al.(1984)

25. SILICA-ENTHALPY MIXING MODEL Steam Fraction did not separate before mixing
The sample points are plotted.
A straight line is drawn from the point representing the non-thermal component of the mixed water (i.e. the point with the lowest temperature and the lowest silica content = point A in Fig.), through the mixed water warm springs (points B and D in Fig.).
The intersection of this line with the qtz solubility curve (point C in Fig.) gives the enthalpy of the hot-water component (at reservoir conditions).
From the steam table, the temperature corresponding to this enthalpy value is obtained as the reservoir temperature of the hot-water component.

26. SILICA-ENTHALPY MIXING MODEL Steam separation occurs before mixing
The enthalpy at the boling temperature (100C) is obtained from the steam tables (which is 419 j/g)
A vertical line is drawn from the enthalpy value of 419 j/g
From the inetrsection point of this line with the mixing line (Line AD), a horizantal line (DE) is drawn.
The intersection of line DE with the solubility curve for maximum steam loss (point E) gives the enthalpy of the hot-water component.
From the steam tables, the reservoir temperature of the hot-water component is determined.

27. SILICA-ENTHALPY MIXING MODEL
In order for the silica mixing model to give accurate results, it is vital that no conductive cooling occurred after mixing. If conductive cooling occurred after mixing, then the calculated temperatures will be too high (overestimated temperatures). This is because:
the original points before conductive cooling should lie to the right of the line AD (i.e. towards the higher enthalpy values at the same silica concentrations, as conductive cooling will affect only the temperatures, not the silica contents)
in this case, the intersection of mixing line with the quartz solubility curve will give lower enthalpy values (i.e lower temperatures) than that obtained in case of conductive cooling.
in other words, the temperatures obtained in case of conductive cooling will be higher than the actual reservoir temperatures (i.e. if conductive cooling occurred after mixing, the temperatures will be overestimated)

28. SILICA-ENTHALPY MIXING MODEL
Another requirement for the use of enthalpy-silica model is that no silica deposition occurred before or after mixing. If silica deposition occurred, the temperatures will be underestimated. This is because:
the original points before silica deposition should be towards higher silica contents (at the same enthalpy values)
in this case, the intersection point of mixing line with the silica solubility curve will have higher enthalpy values(higher temperatures) than that obtained in case of silica deposition
in other words, the temperatures obtained in case of no silica deposition will be higher than that in case of silica deposition (i.e. the temperatures will be underestimated in case of silica deposition)

29. CHLORIDE-ENTHALPY MIXING MODEL
Fig.6. Enthalpy-chloride diagram for waters from Yellowstone National Park. Small circles indicate Geyser Hill-type waters and smal dots indicate Black Sand-type waters (From Fournier, 1981).

30. CHLORIDE-ENTHALPY MIXING MODEL
ESTIMATION OF RESERVOIR
TEMPERATURE
Geyser Hill-type Waters
A = maximum Cl content
B = minimum Cl content
C = minimum enthalpy at
the reservoir
Black Sand-type Waters
D = maximum Cl content
E = minimum Cl content
F = minimum enthalpy at
Enthalpy of steam at 100 C =
2676 J/g (Henley et al., 1984)

31. CHLORIDE-ENTHALPY MIXING MODEL
ORIGIN OF WATERS
N = cold water component
C, F = hot water components
F is more dilute & slightly cooler than C
F can not be derived from C by process of mixing between hot and cold water (point N), because any mixture would lie on or close to line CN.
C and F are probably both related to a still higher enthalpy water such as point G or H.

32. CHLORIDE-ENTHALPY MIXING MODEL
ORIGIN OF WATERS
water C could be related to water G by boiling
water C could also be related to water H
by conductive cooling
water F could be related to water G or water H by mixing with cold water N

34. ISOTOPES IN GEOTHERMAL EXPLORATION & DEVELOPMENT

35. ISOTOPE STUDIES IN GEOTHERMAL SYSTEMS
At Exploration, Development and Exploitation Stages
Most commonly used isotopes
Hydrogen (1H, 2H =D, 3H)
Oxygen (18O, 16O)
Sulphur (32S, 34S)
Helium (3He, 4He)

36. ISOTOPE STUDIES IN GEOTHERMAL SYSTEMS
Geothermal Fluids
Sources
Source of fluids (meteoric, magmatic, ..)
Physico-chemical processes affecting the fluid comosition
Water-rock interaction
Evaporation
Condensation
Source of components in fluids (mantle, crust,..)
Ages
(time between recharge-discharge, recharge-sampling)
Temperatures (Geothermometry Applications)

37. Sources of Geothermal Fluids
H- & O- Isotopes
Physico-chemical processes affecting the fluid composition
Sources of components (elements, compounds) in geothermal fluids
He-Isotopes (volatile elements)

38. Sources of Geothermal Fluids and Physico-Chemical Processes
STABLE
H- & O-ISOTOPES

39. Sources of Geothermal Fluids Stable H- & O-Isotopes
2H (D) = %
D/H
16O = % 99.76
17O = % 0.04
18O = % 0.20
18O / 16O

40. Sources of Geothermal Fluids Stable H- & O-Isotopes
(D/H)sample- (D/H)standard
 D () = x 103
(D/H)standard
(18O/16O)sample- (18O/16O)standard
 18O () = x 103
(18O/16O)standard
Standard = Standard Mean Ocean Water
= SMOW

41. Sources of Geothermal Fluids Stable H- & O-Isotopes
(D/H)sample- (D/H)SMOW
 D () = x 103
(D/H)SMOW
(18O/16O)sample- (18O/16O)SMOW
 18O () = x 103
(18O/16O)SMOW

42. Sources of Geothermal Fluids Stable H- & O-Isotopes
Sources of Natural Waters:
Meteoric Water (rain, snow)
Sea Water
Fossil Waters (trapped in sediments in sedimanary basins)
Magmatic Waters
Metamorphic Waters

43. Sources of Geothermal Fluids Stable H- & O-Isotopes

44. Sources of Geothermal Fluids Stable H- & O-Isotopes

45. Sources of Geothermal Fluids Stable H- & O-Isotopes

46. Sources of Geothermal Fluids Stable H- & O-Isotopes

47. Physico-Chemical Processes: Stable H- & O-Isotopes
Latitute 
dD d18O
Altitute from Sea level 

48. Physico-Chemical Processes: Stable H- & O-Isotopes
Aquifers recharged by precipitation from lower altitutes higher dD - d18O values
Aquifers recharged by precipitation from higher altitutes lower dD - d18O values
Mixing of waters from different aquifers

49. Physico-Chemical Processes: Stable H- & O-Isotopes
Boiling and vapor separation 
dD d18O in residual liquid
Possible subsurface boiling as a consequence of pressure decrease (due to continuous exploitation from production wells)

50. Monitoring Studies in Geothermal Exploitation
Any increase in dD - d18O values 
due to sudden pressure drop in production wells
recharge from (other) aquifers fed by precipitation from lower altitutes
subsurface boiling and vapour separation
Aquifers recharged by precipitation from lower altitutes higher dD - d18O
Aquifers recharged by precipitation from higher altitutes lower dD - d18O
Boiling and vapor separation 
dD d18O in residual liquid

51. Monitoring Studies in Geothermal Exploitation
Monitoring of isotope composition of geothermal fluids during exploitation can lead to determination of, and the development of necessary precautions against
Decrease in enthalpy due to start of recharge from cold, shallow aquifers, or
Scaling problems developed as a result of subsurface boiling

52. (Scaling) Vapour Separation Volume of (residual) liquid 
Concentration of dissolved components in liquid 
Liquid will become oversaturated
Component (calcite, silica, etc.) will precipitate
Scaling

53. Dating of Geothermal Fluids
3H- & 3He-ISOTOPES

54. Dating of Geothermal Fluids
Time elapsed between Recharge-Discharge or Recharge-Sampling points (subsurface residence residence time)
3H method
3H-3He method

55. TRITIUM (3H)
3H = radioactive isotope of Hydrogene (with a short half-life)
3H forms
Reaction of 14N isotope (in the atmosphere) with cosmic rays
147N + n  31H C
Nuclear testing
3H concentration
Tritium Unit (TU)
1 TU = 1 atom 3H / 1018 atom H
3H  3He + 
Half-life = year
Decay constant () = y-1

56. 3H – Dating Method
3H concentration level in the atmosphere has shown large changes
İn between 1950s and 1960s (before and after the nuclear testing)
Particularly in the northern hemisphere
Before 1953 : TU
In 1963 : 3000 TU

57. 3H – Dating Method N=N0e-t 3H0 (before 1963)  10 TU
3H-concentration in groundwater < 1.1 TU
Recharge by precipitations older than nuclear testing
3H-concentration in groundwater > 1.1 TU
Recharge by precipitations younger than nuclear testing
N=N0e-t H0 (before 1963)  10 TU
3H= 3H0e-t  = y-1
t = = 40 years
 3H  1.1 TU

58. 3H – Dating Method APPARENT AGE 3H= 3H0e-t
3H = measured at sampling point
3H0 = measured at recharge point
(assumed to be the initial tritium concentration)
 = y-1
t = apparent age

59. 3H – 3He Dating Method t = 1/ * ln (3He/3H + 1)
3He = 3H0 – 3H (D = N0-N)
3H= 3H0 e-t (N = N0e -t)
3H0= 3H et
3He = 3H et - 3H = 3H (et – 1)
t = 1/ * ln (3He/3H + 1)
3He & 3H – present-day concentrations measured in water sample

60. Geothermometry Applications
Isotope Fractionation – Temperature Dependent
Stable isotope compositions 
utilized in Reservoir Temperature estimation
Isotope geothermometers
Based on: isotope exchange reactions between phases in natural systems
(phases: watre-gas, vapor-gas, water-mineral.....)
Assumes: reaction is at equilibrium at reservoir conditions

61. Isotope Geothermometers
12CO2 + 13CH4 = 13CO2 + 12CH4 (CO2 gas - methane gas)
CH3D + H2O = HDO + CH4 (methane gas – water vapor)
HD + H2O = H2 + HDO (H2 gas – water vapor)
S16O4 + H218O = S18O4 + H216O (dissolved sulphate-water) 
1000 ln  (SO4 – H2O) = 2.88 x 106/T2 – 4.1
(T = degree Kelvin = K )

62. Isotope Geothermometers
Regarding the relation between mineralization and hydrothermal activities
Mineral Isotope Geothermometers
Based on the isotopic equilibrium between the coeval mineral pairs
Most commonly used isotopes: S-isotopes

63. Suphur (S)- Isotopes (34S/32S)sample- (34S/32S)std.
 34S () = x 103
(34S/32S)sample
Std.= CD
=S-isotope composition of troilite (FeS) phase in Canyon Diablo Meteorite

64. S-Isotope Geothermometer
34S = 34S(mineral 1) - 34S(mineral 2)
34S = 34S= A (106/T2) + B